an unstretched hanging spring is 50cm long. suspending a 100N weight from it makes its lenght 60cm. Adding another 100N weight will make the spring --
60cm, 70 cm, 80 cm, 100 cm, or 120 cm.
No idea how they came up with any of the five ??? My answer was different!
Please help!
The amount of stretching is proportional to the weight applied. That's called Hooke's law.
Since 100N stretches the spring 10 cm, 200 N will stretch it 20 cm. Add that to the original unstretched length.
50 + 20 = ___ cm
To solve this problem, we can use Hooke's Law, which states that the extension of a spring is directly proportional to the force applied to it. The formula for Hooke's Law is given by:
F = kx
where F is the force applied to the spring, k is the spring constant, and x is the extension of the spring.
Given that the unstretched length of the spring is 50 cm and suspending a 100 N weight from it makes its length 60 cm, we can calculate the extension of the spring using the following equation:
Extension = Final Length - Unstretched Length
Extension = 60 cm - 50 cm
Extension = 10 cm
Now, we can use this extension value to find the spring constant (k) using Hooke's Law. Let's rearrange the formula as follows:
k = F / x
k = 100 N / 10 cm
k = 10 N/cm
Now, if we add another 100 N weight to the spring, we can calculate the new length of the spring using Hooke's Law:
F = kx
200 N = (10 N/cm) * x
x = 200 N / 10 N/cm
x = 20 cm
By adding another 100 N weight, the spring will extend by 20 cm. Therefore, the new length of the spring will be:
Final Length = Unstretched Length + Extension
Final Length = 50 cm + 20 cm
Final Length = 70 cm
Therefore, the correct answer is 70 cm.
To solve this problem, we can use Hooke's Law, which states that the force needed to extend or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.
Let's break it down step by step:
1. First, we know that the unstretched length of the spring is 50 cm.
2. Next, when a 100N weight is suspended from the spring, its length becomes 60 cm. This means that the weight caused a change in length of 60 cm - 50 cm = 10 cm.
3. Using Hooke's Law, we can write down the equation: F = k * x.
- F is the force applied to the spring (100N in this case)
- k is the spring constant (which we'll find out)
- x is the displacement or change in length of the spring (10 cm in this case)
4. Rearranging the equation, we get: k = F / x, where k is the spring constant.
Plugging in the values, we have k = 100N / 10 cm = 10 N/cm.
5. Now, adding another 100N weight would double the force being applied to the spring. This results in a new force of 100N + 100N = 200N.
6. Using Hooke's Law again: F = k * x, where F is the new force (200N), and k is still 10 N/cm (from step 4).
7. Rearranging the equation to solve for x (change in length), we get: x = F / k.
Plugging in the values, we have x = 200N / 10 N/cm = 20 cm.
8. Finally, to find the total length of the spring when the second weight is added, we add the displacement (20 cm) to the original length of 50 cm.
The total length of the spring will be 50 cm + 20 cm = 70 cm.
Therefore, the correct answer is 70 cm.